Apparatus and method for metering sub-10 cc/minute liquid flow

ABSTRACT

Apparatus for accurately metering liquid flow based on the injection of a brief heat pulse into the flowing stream, e.g., via a miniature thermistor, and detection of an electronic time derivative of temperature downstream with, e.g., a second microprobe thermistor. This detection triggers a subsequent heat pulse and the cycle repeats, with pulse total corresponding to elapsed liquid throughput, and pulse frequency to flow rate.

This is a continuation of application Ser. No. 280,668, filed July 6,1981, now U.S. Pat. No. 4,532,811.

BACKGROUND OF THE INVENTION

In order to determine molecular weight or size distribution of separatedparticles in GPC (Gel Permeation Chromatography) and HDC (HydrodynamicChromatography), peak composition is inferred from its elution volume.Elution volume has been determined in chromatography by measuring thetransit time of unretarded marker species to which the detector issensitive and ratioing solute position to marker position. Use of amarker is quite typical since even premium quality liquidchromatographic pumps are generally not capable of better than 0.3% flowstability over repeated analyses. For this reason, the practice ofassuming constant flow and measuring elution time would frequentlyresult in unacceptable uncertainties in the determination of latexparticle diameters as an illustrative example.

Another flow related source of error for concentration-sensitivedetectors (UV, IR, RI, Conductivity) in LC is the inverseproportionality between peak area and flow rate, e.g., a 0.5% flowdecrease produces a 0.5% area increase.

The most troublesome flow fluctuations are those with periods on theorder of peak widths since these cause individual peak areas to change.Such fluctuations can occur, e.g., with reciprocating piston pumpsbecause check valve leakage rates tend to change for subsequent pumpstrokes, and stroke volumes are typically 50 to 500 μl.

Present methods for measuring elapsed flow include collecting a volumeof eluent in a graduated cylinder, measuring the movement of a bubbleinjected into the flowing liquid, or accumulating the total number ofdumps of a siphon dump counter, all techniques which can be somewhatimprecise or erratic.

Other classical flow measuring devices, generally for higher ranges,include the following:

1. Coriolis flow meter, measures mass flow as a function of gyroscopictorque forces. This method is complex and expensive; accuracy is ±0.4%.

2. Ultrasonic flow meter, suited for gallons-per-minute flow; accuracyis ±0.5%.

3. D/P flow cell, measures pressure drop across an orifice. Prone toplugging, drift; viscosity dependent.

4. Turbine meter, target meter, venturi meter, rotameter, Pitot tube,all principally applicable to flow rates in excess of 50 cc/min.

5. Continuous heat addition flow meter, heats eluent and measuresdownstream temperature continuously. Result varies with the specificheat of the metered liquid and ambient temperature fluctuations.

6. Self-heating thermistor, undergoes cooling proportional to flow.Nonlinear and result varies with specific heat of solution and ambienttemperature variations.

THE INVENTION

The invention relates to a non-invasive liquid metering method andapparatus for determining liquid movement with an attainable precisionof ±0.1% under typical LC conditions. The invention particularlysatisfies the technical need for an improved liquid metering method andapparatus for accurately metering liquids in the 0.1 to 10 cc/minuterange where metering precision becomes extremely important.

The inventive method and apparatus uses the principle of injecting aheat pulse into the flowing stream via, e.g., a miniature self-heatingthermistor (or semiconductor) and detecting the pulse downstream with,e.g., a second microprobe or fast response thermistor. Pulse detectiontriggers a subsequent heat pulse upstream and the process repeats, withpulse total corresponding to elapsed liquid throughput and pulsefrequency to flow rate.

Salient keys to achieving this technical advance in flow meteringinclude particularly:

1. minimizing the thermal mass of the heat "pulser" and sensor throughthe application of semiconductor pulsing and sensing elements;

2. electronically time-differentiating the sensor output to rejectcharacteristically slower ambient thermal drift and to minimize responsetime in preparation for subsequent pulse detection;

3. application of a flow metering scheme which uses an improved methodfor high precision flow measurements and flow cell calibration; and

4. development of a flow cell and method, which by component selectionand operation, is highly independent of temperature and liquidcomposition variables.

While the general principle of heat pulse injection is not entirely newto liquid metering, being applied previously in the form of what isknown as "Knauer Electronic Volumeter" distributed through UtopiaInstrument Company, Joliet, Ill., none of the recited technicalimprovements (1-4) are embodied in this prior liquid meter. Among majorexpressed differences in utility between the invention and the priormeter, as taken from the manufacturer's literature, is the developmentof a successful two-probe metering flow cell (Knauer teaching utilityonly with respect to a 4 probe device); as well as the extended utilityto meter aqueous solvents, a field of utility disclaimed in themanufacturer's literature.

SUMMARY OF THE INVENTION

The invention as it relates to an electronic flow cell for accuratelymetering liquid, more specifically comprises in combination:

(a) a flow cell having a flow-through passage;

(b) a resistance heat means comprising a semiconductor element, theresistance heating means having a heat emitting surface which is exposedin the flow passage; and

(c) a heat sensing thermistor, the heat sensing thermistor having a heatsensing surface exposed in the flow passage in fixed, spacedrelationship with the heat emitting surface of the resistance heatingmeans.

The invention as it relates to the inventive flow cell, together withthe electronic circuit to operate same, comprises in combination:

(a) a flow cell having a flow through passage;

(b) a resistance heating means comprising a semiconductor heatingelement, and circuit means to operate the semiconductor element as aresistance pulse heater, the resistance heating means having a heatemitting surface which is exposed in the flow passage;

(c) a heat sensing thermistor, and circuit means to operate thethermistor in the heat sensing mode, the heat sensing thermistor havinga heat sensing surface which is exposed in the flow passage in fixed,spaced relationship with the heat emitting surface of the resistanceheating means;

(d) a differentiating circuit means for outputting an electrical pulsesignal which in magnitude is proportional to dR_(t) /dt, or a timederivative thereof, wherein dR_(t) /dt is the time rate of change of theresistance of the heat sensing thermistor with pulse temperature changesin the liquid to be metered;

(e) said circuit means operating the resistance heating means comprisinga timer circuit means which is activated directly or indirectly by eachevent of a sensible outputted pulse of circuit means (d), to apply atimed voltage pulse to the resistance heating means.

The invention further relates to an improved method for electronicallymetering the flow of Newtonian liquids which comprises:

(a) conveying the liquid to be metered through an electonic flow cellhaving a predetermined calibrated cell volume (V_(c)) and calibratedtime constant (K);

(b) inputting uniformly timed heat pulses into the conveyed liquid anddetecting the pulses downstream, and wherein each detection eventtriggers the input of a timed heat pulse to produce the condition ofpulse frequency being related to liquid flow rate (f);

(c) electronically detecting the period (T) between pulses; and

(d) determining a measure of flow of the metered liquid based on theapplication of the relationship,

    T=(V.sub.c /f)+K

Optimum forms of the apparatus invention use a self-heating thermistoras the heat pulsing element, in conjunction with a fast responsethermistor as the heat sensor, each of which includes an electricalinsulator, e.g., of glass, which encapsulates the semiconductorthermistor element thereof. In addition, not less than the second timederivative of the resistance of the heat sensing thermistor is taken andused as the signal to pulse the self-heating thermistor.

In respect to the inventive method, other known forms of electronic flowcells (i.e., "flow cells", the metering principle of which is based onthe time of flight of electronically injected heat pulses) can beoperated by the method to produce an improved measure of flow. Theoptimum form of practice of the method invention uses the inventiveelectronic flow cell. The term Newtonian liquids as used in the methodterminology refers to a liquid, the viscosity of which at the meteredflow condition is substantially constant.

While the invention has been described with regard to applications whereactual data is desired to show, as a measure of flow, instantaneous oraveraged flow rate or total flow volume with time, the invention canadditionally be applied in the form of a control method or instrument,e.g., to regulate a chromatographic or other liquid metering pump, e.g.,by continually detecting flow rate and relaying a signal (measure offlow) to the pump to adjust its flow to a metered setting. It is alsoapparent that while the major expressed technical need is for improvedapparatus and method to meter flow in the sub-10 cc/minute range, theprinciples of the invention are extendable to measuring a considerablyhigher range of flow rates as Example 3 demonstrates below.

DRAWING

Yet further features and advantages of the invention will be apparentfrom the "Detailed Description of the Invention", below, taken with theaccompanying drawing wherein:

FIG. 1 is an exploded, partly cross-sectioned view of a preferentialflow cell design for metering liquid according to the principles andteachings of this invention;

FIG. 2 is a top view showing the cell body of the FIG. 1 flow cell;

FIG. 3 is a schematic of a preferred electronic circuit for operatingthe flow cell according to the principles of the method of theinvention; and

FIG. 4 is a graph associated with the calibration of the flow cell asdescribed in Example 1.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIGS. 1 and 2, a preferred embodiment of the apparatus ofthe invention is illustrated comprising an electronic flow cell 10 foraccurately metering milliliter liquid movement (herein meaning the rangeof about 0.1 to 10 cc/min). Flow cell 10 comprises a narrow flow-throughchannel or passage 12 through which the liquid to be metered is flowed.The size or internal volume of the flow cell (calibrated) is fixed andwithin the range of from between about 0.01 to 0.5 cc, preferably about0.1 to 0.25 cc.

Mounted fixedly in the body 14 of flow cell 10 is a thermistor 16 (orits equivalent as described hereinafter) which is designed to be used inthe self-heating mode to impart brief, sensible heat pulses to theliquid to be metered. The self-heating thermistor is comprised of a heatemitting surface 18 which is exposed to the flow channel for makingdirect flow contact with the liquid to be metered.

Spaced a fixed distance from the self-heating thermistor is a preferablysmaller mass thermistor 20 which, in relative terms, is a fast responsethermistor designed for use in the heat sensing mode. The heat sensingthermistor is comprised of a heat sensing surface 22 which is stationaryand exposed in flow channel 12, also for making direct flow contact withthe liquid to be metered (downstream from the self-heating thermistor).

Preferentially used for the self-heating thermistor is what is referredto as a "standard probe" thermistor, various commercial types of whichare described in the trade publication entitled "Thermistor Manual"(Copyright 1974; and also bearing the identifying code number "EMC-6"),this publication being available from Fenwall Electronics, Framingham,Mass., and being incorporated fully herein by reference.

These standard probe thermistors are characteristically available in thedesirable form comprising a glass bulb or probe, given Reference Numeral24 in the drawing, and which comprises the heat emitting surface of thethermistor. Encased in the glass probe is a semiconductor element 26which is thus protected and electrically insulated from direct contactwith the liquid to be metered. The glass encased semiconductor elementor probe 24 of this preferential thermistor type measures 0.100" indiameter. It can be used to develop approximately 50-150 milliwatts peakpower over extended use periods without apparent deterioration oralteration of its electrical properties. Its small thermal mass,indicated by its Time Constant rating (T.C.) in air of between about14-22 seconds is found generally sufficient to permit rapid enoughpulsing in liquid to be suited for application to the invention; and itspower output sufficient to develop sensible heat pulses in conjunctionwith the heat sensing capability of thermistor 20.

Preferentially selected as the heat sensing thermistor 20 is whatFenwall refers to as its "fast response" glass probe thermistor, alsocomprised of a semiconductor element 28 encased in a glass bulb or probe30. These thermistors, due to a much smaller thermal mass, have a T.C.rating in air of about 5 seconds or less.

The commercial heat sensing thermistors described generally have a 3-4percent/°C. negative temperature coefficient. This range of sensitivityhas been found quite suitable for use in the invention. A lessertemperature coefficient for the heat sensing thermistor would beoperable so long as sufficient resistance change is registered to sensethe heat pulses in the liquid.

As should be readily apparent, the temperature coefficient of theself-heating thermistor is largely an unimportant parameter since thisthermistor is used in the self-heating mode; it being preferred,however, to use a self-heating thermistor with a negative temperaturecoefficient to minimize possible thermistor damage due to inadvertentexcessive heating, e.g., in the event the apparatus is abused oroperated improperly. Either a negative or positive temperaturecoefficient thermistor may be equivalently used as the heat sensingthermistor.

As mentioned previously, the invention contemplates equivalents to theself-heating thermistor. These would be based on the substitution forthermistor element 16, of a semiconductor based heating element whichdiffers in that it does not possess the temperature coefficient propertywhich characterizes a thermistor element. The term "semiconductor" isintended to define a material which has a resistivity in the range ofabout 10³ to 10¹³ μ ohm-centimeters, most preferably, about 10⁴ to 10⁶ μohm-centimeters. Marginally useful as element 26 are resistance heatingelements, the resistivity of which falls within the transition rangebetween conductors and semiconductors, i.e., from about 750-1000μohm-centimeters. The term "semiconductors", as used in this disclosure,is by definition intended to include such latter materials having aresistivity within the defined transition range (e.g, certain carbonbased materials); and which may be suitably fabricated into resistanceheating elements useful for the purposes of the invention.

CELL FABRICATION

As can be readily appreciated, a very advantageous feature of flow cell10 is its simplicity in design and fabrication. A preferred flow cell isconstructed using a machinable block of glass filled Teflon® tofabricate cell body 14. Ordinary drilling methods may be used to defineflow channel 12. In addition, threaded openings 32, 34 are tapped ateach end of the cell body for attaching chromatographic tube endfittings 36, 38 for passing liquid to be metered through flow channel12; and similar threaded openings 40, 42 are tapped in the cell body atpositions normal to the flow channel for threadably mounting thethermistors 16, 20, respectively.

Due to the relatively large size of the self-heating thermistor, a smalldepression 44 is sunk in cell body 14 immediately below the lower tip ofheat emitting surface 18. The depression permits the heat emittingsurface of the self-heating thermistor to be adjustably moved forcentering on the axis of flow channel 12 for alignment with heat sensingsurface 22 of the heat sensing thermistor (which is similarly desirablycentered on the axis of the flow channel). Where relative dimensionsrequire, the flow channel can be enlarged at the position of either orboth thermistors 16, 20 to produce a coaxial step enlarged cavity inwhich the heat emitting and heat sensing surfaces of the thermistors areplaced in centering alignment with the axis of the flow channel. Theflow channel between the thermistors is correspondingly relatively smallin diameter, to produce a flow cell of correspondingly small(calibrated) volume. The small size flow cells are also beneficiallyfabricated by mounting thermistors 16, 20 on opposite sides of cell body14 whereby, through the offset, a closer spacing and thus shorter flowchannel length dimension can be defined using essentially the same flowcell design as illustrated in the drawing.

A preferred arrangement for threadably affixing thermistors 16, 20 incell body 10 employs hollow threaded plugs 46, 48, preferably ofplastic, through which the electrical lead wires of the thermistors 16,20 are passed. Elastic O-rings 50, 52, suitably of Kalrez®, are seatedin threaded openings 40, 42, respectively, and compressed to form aliquid tight seal about the glass thermistor body of each thermistor. Aterminal strip 54 is attached, e.g., by machine screws, to the cellbody. The lead wires of the thermistors are fastened, e.g., by standardelectrical contact screws, to the terminal strip.

Obviously, considerable variation in this simple cell design is possiblewithout changing it functionally. For example, the cell body may becomposed of several joined components (as opposed to the unitary blockconstruction shown). In addition, the cell flow channel may be definedusing, e.g., a narrow diameter plastic tube (an embodiment described inthe teaching Example 3, below).

FLOW RESTRICTOR

A flow restrictor or restrictor means 56 is connected by chromatographictube end fitting 38 to the outfeed port or opening 34 of flow cell 10.The flow restrictor suitably comprises an appropriate length ofcapillary tubing which restricts flow to produce back pressuresufficient to avoid minute degassing of the metered liquid. The flowrestrictor is beneficially used whenever the flow cell is located in aposition of insufficient back pressure to avoid detrimental degassingphenomena. Any alternative device such as a common restrictor valve maybe equivalently substituted for the illustrated capillary tube. The useof the flow restrictor, while optional, produces optimum levels ofliquid metering precision in combination with flow cell 10 when used,e.g., to monitor chromatographic column effluent flow (wherecharacteristically low back pressure leads to deterimental degassing ofthe metered liquid).

ELECTRONICS

A preferred design of an electronic circuit for operating flow cell 10is shown in FIG. 3 and comprises circuit means 58 for operatingthermistor 20 in the heat sensing mode. Circuit means 58 comprises astandard voltage divider circuit consisting of a potentiometer 60 and aseries resistor 62 divided at juncture A from thermistor 20 and seriesresistors 64, 65. The total resistance of the circuit is sufficient toproduce negligible current pulse surges due to pulse resistancedecreases of the thermistor, and hence, non-detrimental self-heating ofthe heat sensing thermistor. The terminals of a common power source areconnected across the voltage divider circuit to provide energizingvoltage within the equilibrium range of thermistor 20. A capacitor 67stabilizes the voltage at juncture A from rapid transients in thepositive voltage supply level.

Pulse temperature changes in the metered liquid are electronicallysensed in the form of positive-going voltage pulses which areproportional to the resistance change of thermistor 20 with temperature(this circuit being designed for and assuming the use of a negativetemperature coefficient heat sensing thermistor). The outputted voltagepulses pass through a series current limiting resistor 66 and areamplified by a non-inverting, e.g., conventional type 741, operationalamplifier 68, set for a gain of 50 by the selected ratio of resistors70, 72 which are set in a voltage divider circuit mode on the negativefeedback of amplifier 68 (in the standard arrangement). An approximatepulse wave form of the pre-amplified and amplified voltage pulse isshown in Inset A-B. This pulse is fed to a preferably two stagedifferentiating amplifier circuit or circuit means 74, 74a. First stage74 of the differentiating circuit comprises a capacitor 76 in serieswith a current limiting resistor 78 and connected to the inverting inputof, e.g., preferentially a type 741, operational amplifier 80. Afeedback resistor 82 returns the input to zero following each inputtedpulse signal. A capacitor 84 is connected in parallel with resistor 82to filter high frequency ambient electrical noise.

The outputted pulse signal of amplifier 80 is both inverted andproportional to the time rate of change of the inputted voltage pulse(of Inset A-B), an approximated wave form of the outputted andderivatized pulse being shown in Inset C. Since the amplified Inset A-Bvoltage pulse is proportional to the electrically sensed resistance ofthe heat sensing thermistor, the outputted pulse (Inset C) is thusequivalently considered as the amplified time rate of change (or firsttime derivative) of the resistance change of thermistor 20 with pulsetemperature changes in the metered liquid.

The time rate of change pulse signal is inputted to the second stage 74aof the differentiating circuit, which consists of the common elements(with amplifier 80) given like reference numerals. Additionally, thenon-inverting input of the second stage amplifier 80a is provided with azero adjustment biasing circuit 84 which is connected to the referencedpower supply outputs in order to trim output of the voltage pulse signalof amplifier 80a. An approximate form of the amplifier 80a, pulse signalis shown for exemplary purposes in Inset D; and is the amplified,electronically derived, second time derivative of the resistance of theheat sensing thermistor 20 with pulse temperature changes in the meteredliquid.

The second derivative voltage pulse is fed through a current limitingresistor 86 to the non-inverting input of, e.g., suitably a type 741operational amplifier 88. Amplifier 88 is connected to a capacitor 90and resistors 92, 94 to produce high gain amplification with additionalhigh frequency filtering. An outputted voltage pulse amplified, e.g.,500 times, is generated by amplifier 88 and filtered through a low passfilter consisting of a resistor 96 and capacitor 98 connected to thepower supply common. The total amplification and derivatizationfunctions produce a square wave curve or voltage pulse form which isshown in Inset E.

The voltage pulse of Inset E is fed to a timer circuit means 100 forpulsing the self-heating thermistor, and which includes a currentlimiting resistor 102, connected to the base of a switching transistor104, suitably a standardized Part No. 2N3904. Transistor 104 switchesits collector terminal 106 from +15 volts (power supply level) to zeroupon arrival of the output of each Inset E voltage pulse. With each suchtriggering of the collector terminal, a voltage pulse from +15 to zerois produced.

The collector terminal at rest is biased at +15 volts by a voltagedivider circuit consisting of a resistor 108 and the switchingtransistor. A second voltage divider 110, 112 produces a highly positivevoltage at rest. The two voltages are placed across a capacitor 114 suchthat the capacitor is at an elevated voltage on both plates. Theswitching of the collector terminal voltage rapidly reduces the voltageat capacitor 114, whereby capacitor plate 116 is pulled to zero brieflyuntil the second voltage divider returns to the rest voltage.Consequently, the voltage pulse width generated at the collectorterminal is reduced to a voltage spike, which is fed to pin #2 of, e.g.,suitably a type 555 timer 118. Pin #2 of the timer is the time cyclereset pin. The timer outputs a voltage pulse at pin #3, the duration ofwhich is determined by an external variable resistor 120 in combinationwith an external capacitor 122 connected to pins #6 and #7 of timer 118.The setting is adjustably changed in this circuit between the limits of0.1 to 1.0 second. Pins # 1 and #8 are connected to common and the +15volts power supply, respectively.

An outputted voltage of fixed duration is fed from pin #3 to a relay124, e.g., suitably a DIP reed relay, which is a double pole, singlethrow relay which completes the contact between the power supply, aseries resistor 126, and the heating thermistor 16. Leads 128, 130connect from the relay to an external data collector 132, e.g., acomputer, which records each activation event of the self-heatingthermistor (in order to derive T). The circuit is initially activated bya manual switch 134. A single 100 ma-rated ±15 volts regulated powersupply may be used to operate the entire circuit.

OPERATION

The liquid metering process is initiated by pushbutton activation of athermal pulse at R_(h) (the self-heating thermistor). The -4%/°C.temperature coefficient of the referenced Fenwall type GP38P12 heatsensing thermistor (R_(t)) produces a positive-going voltage at junctureA as the warm liquid pulse traverses the sensing zone. This signal isamplified at B and connected through capacitor 76 to the inverting inputof amplifier 80 of the first stage differential amplifying circuit 74.This arrangement yields a pulse voltage output at C equivalent to theamplified inverted time derivative at B. Output at C is proportional todR_(t) /dt and thus slow temperature changes yield essentially zeroresponse in contrast to heat pulses generated in situ by theself-heating thermistor.

A single derivative pulse output returns to baseline too slowly to beoptimally prepared for subsequent pulses. Most preferably, therefore, aninverted second derivative is produced at the second stage amplifier 80aresulting in the approximate pulse output form shown in Inset D andwhich is proportional to d² R_(t) /dt².

This voltage pulse form is amplified at E to drive the transistortriggered timing circuit that applies power to the reed relay. Thisrelay supplies a +30 volt D.C. pulse for a fixed time interval(generally 0.1 to 1.0 second) to both the pulse counter (i.e.,computer), and self-heating thermistor 16. Metering precision isimproved through the use of a D.C. pulse form, as opposed to an A.C.voltage pulse to heat thermistor 16. The 2K ohm resistor 126 protectsthe self-heating thermistor from overheating damage as it tails intoself-heating and reduced resistance. A calculated maximum of 113 mW ofpower is dissipated at R_(h) during application of the +30 volts D.C.power, using the referenced Fenwall GB34P2 standard probe thermistor.

The rate of flow and/or total flow of the metered liquid iselectronically computed based on the pulse data collected by theelectronics, and by applying the following generic mathematicalexpression:

    T=V.sub.c /f+K

where:

T=time period between pulses (e.g., in seconds);

V_(c) =calibrated cell volume constant (e.g., in cubic centimeters);

f=flow rate (e.g., in cubic centimeters per second); and

K=calibrated time constant (e.g., in seconds).

The values V_(c) and K may be determined, e.g., by the exemplary flowcell calibration procedure described in Example 1. T is the pulse perioddata collected, whereas f is solved to derive the flow rate of themetered liquid. Since the value V_(c) /f is shown to becharacteristically linear with T over a wide flow rate range (seeExample 1), the computation of f may be straightforwardly performedelectronically; and by a chart recorder or other device displayedvisually in any desired form, e.g., to display either or both theinstantaneous or averaged flow rate, or to produce based on total pulsecounter (ΣT), total flow of the metered liquid over any elapsed periodof time.

EXAMPLE 1 Calibration

This Example describes a preferential calibration method suitable todetermine the calibration constants V_(c) and K. These constants aredescribed with respect to a given flow cell, electronic circuit, andelectronic settings. In this study, the flow cell is of a design inwhich the thermistors 16, 20 are set apart (in center-to-center spacing)approximately 11/2 inches; and are used in conjunction with a flowchannel 12 of approximately 1/16 inch in diameter. Timer 118 is set toproduce 0.8 second pulse heating time; and potentiometer 60 is adjustedto provide a steady state 50 mV positive baseline voltage on which thepositive-going voltage pulses of the heat sensing thermistor areimposed. The zero adjust biasing circuit 84 is adjusted to produce zerovoltage at D during the absence of pulsing.

Apparatus used to calibrate the flow cell consists of a Constametric Ipump from LDC Corporation. The pump withdraws liquid (water) from achromatographic reservoir, and advances it at a preset rate of flowthrough, sequentially, a pressure gauge, pulse dampening coil, andultimately the flow cell, using standard 1/16 inch O.D. chromatographictubing to convey the liquid. The discharge from the flow cell is fedthrough a back pressure-applying capillary coil (3"×0.005" I.D.capillary) to a collection vessel. A timer is used with a high precisionbalance to verify liquid flow rates.

The data generated are complied in Table I, below, wherein: f is theaveraged flow rate in cc/minute determined from the precision balanceand timer; and T is the averaged time period in seconds between pulsingof the self-heating thermistor as determined from relay 124.

                  TABLE I                                                         ______________________________________                                        Experiment f          l/f        T                                            Run Number cc/min     (seconds/cc)                                                                             (seconds)                                    ______________________________________                                        1          5.30       11.321     1.1826                                       2          4.78       12.552     1.2384                                       3          4.25       14.118     1.3078                                       4          3.74       16.043     1.3987                                       5          3.20       18.750     1.5240                                       6          2.64       22.727     1.7020                                       7           2.125     28.235     1.9729                                       8          1.61       37.267     2.4327                                       9          1.06       56.604     3.3449                                       ______________________________________                                    

Knowing f and T from any two sets of data points, taken from Table I,the equation T=V_(c) /f+K can be solved to yield the calibrationconstants V_(c) and K, using simultaneous equation solving methods todetermine the two unknowns. For the given flow metering systemdescribed, and using the Table I data, the calibrated cell volume V_(c)is computed to be 0.048 cc; and the calibration constant K is computedto be 0.630 second. Hence, flow in cc/second is determined according tothis flow cell, using the expression

    T.sub.sec =(0.048 cc/f)+0.630 sec.

The validity of the above equation is further established by making theplot illustrated as FIG. 4. The data points of multiple solutions to theequation at varying T_(sec) and f_(cc/min) produce the straight line(slope of V_(c)) which is projected to intercept the ordinate axis atthe value K. Thus, the equation shows that the linear y=mx+brelationship is closely followed. The correlation coefficient for thisdata is calculated to be 0.99989.

Use of the mathematical basis described above to calibrate the flow cellconstants produces exceptional liquid metering precision as shown inExample 2. Nevertheless, liquid flow may be alternatively measured usingthe flow cell with conventional calibration methods, e.g., by equatingtotal pulse count and pulse frequency data, taken from relay 124, topreknown accumulated liquid volumes or flow rates, as applies. Theselatter calibration methods can be applied, for example, in order to usethe flow cell for metering accurately non-Newtonian fluids.

EXAMPLE 2 Precision

The precision of an electronic flow cell of the same design as used inExample 1 is studied by connecting the cell to an elevated eluentreservoir through 5 feet of standard wall 1/16 inch O.D. chromatographictubing. Liquid (water) is fed by gravity feed through the flow cellunder a hydrostatic head pressure (total) of 6 inches of water. Thewater is dispelled ultimately to a collection vessel through tubing(also 1/16" O.D.) which has its end immersed in water in the collectionvessel. Initial liquid flow is at approximately 1 cc/minute, anddiminishes very slightly during the course of the experiment.

The time value of each pulse T produced at relay 124 is electronicallystored in the memory bank of a MINC LSI-11 Microcomputer. At thecompletion of data collection, the computer electronically generates alinear regression curve and computes the standard deviation of T to be2.973 milliseconds. Precision is calculated from the observed standarddeviation to be 0.092% at the 63% confidence level (±1 sigma).

Since it is assumed that actual flow varied randomly (in very smallamounts), due solely to the imperfect characteristics of the testingapparatus, observed precision is thus determined to be no worse than0.092% in this experiment and quite likely true precision is better.

EXAMPLE 3 Range

The various flow cells used in this study essentially differ only inrespect to calibrated cell volume (V_(c)). Flow cells Nos. 1 and 2 ofTable II, below, are constructed using 24 and 12 inches, respectively,of 0.031 inch I.D. tubing which is connected between flow cell blockseach singularly mounting a thermistor. These are the relatively largevolume cells. Cells Nos. 3 and 4 are smaller volume cells of the designshown in FIGS. 1 and 2; flow cell No. 3 being that used in the precedingExample 1. A variable liquid chromatographic metering pump is used todetermine the dynamic flow range specific to each cell design, theobserved results being reported in Table II.

                  TABLE II                                                        ______________________________________                                                                            Observed T                                                                    Average In                                Flow                       Calculated                                                                             Seconds @                                 Cell   K         V.sub.c /V.sub.g *                                                                      Flow Range                                                                             Flow Range                                No.    in seconds                                                                              in cc     in cc/min                                                                              Limits                                    ______________________________________                                        1      0.687     0.492/0.424                                                                             9.84+    3.69 @ flow                                                                   minimum                                   2      0.689     0.219/0.225                                                                             4.56-11.0                                                                              3.63-1.88                                 3      0.630     0.048/0.075                                                                             1.05-5.30                                                                              3.34-1.18                                 4      0.653     0.017/0.025                                                                             0.20-2.17                                                                              5.72-1.12                                 ______________________________________                                         *V.sub.g = geometric cell volume                                         

The largest volume cell No. 1 shows a threshold (minimum) flow detectionlimit at about 10 cc/minute, its upper limit not being treated due tothe limitations of the pumping apparatus used in the experiment. Thisflow cell demonstrates the feasibility of extending the liquid flowmetering principles of the invention to the metering of considerablygreater than 10 cc/minute flow rates.

Flow cells Nos. 1-3 collectively demonstrate the utility of theinvention for metering liquid across essentially the entire practicalscope of the sub-10 cc/minute flow range. This experiment is notintended to be construed to represent an optimization study of flow celldynamic operating range as to any given cell design used in theexperiment.

A point to be noted is that the K values determined for the various flowcells 1-4 are not identical. The slight discrepancies between theobserved K values can probably be attributed to small differences in theelectrical characteristics of the thermistors 16, 20 of each flow cellwhich, while of identical manufacturing source and part description,would be expected to vary slightly in thermal mass and/or electricalproperties.

What is claimed is:
 1. A method of non-invasive liquid metering todetermine the volumetric flow rate of small quantities of a flowingliquid passing through a small elongate channel having a volumecorresponding to a calibrated cell volume (V_(c)) of about 0.5 cc orless, the method comprising the steps of:(a) introducing a heat pulseinto a flowing stream; (b) detecting the heat pulse downstream with atemperature sensitive element to produce an electrical sensor output;(c) electronically time differentiating the sensor output to rejectslower ambient thermal drift and minimize response time in preparationfor subsequent pulse detection, said time differentiating eventproducing an electrical signal which in magnitude is proportional to thesecond or a higher order time derivative of the sensor output; (d) usingthe time differentiated sensor output to trigger a subsequent heat pulseupstream; (e) repeatedly continuing steps (b), (c) and (d); (f)measuring the time intervals between successive pulses; and (g)determining the volumetric flow rate of the liquid through the elongatechannel based on the measured time intervals between successive pulses.2. The method of claim 1, including contacting the liquid with a heatemitting probe positioned within the channel to introduce said heatpulses, and contacting the liquid with a heat sensing probe positionedwithin the channel a fixed distance from the heat emitting probe todetect the heat pulses downstream.
 3. The method of claim 2 wherein theheat emitting probe comprises a semiconductor element, and the heatsensing probe comprises a thermistor element.
 4. The method of claim 3wherein said probe elements are encased within an insulative claddingmaterial.
 5. Apparatus for metering sub-10 cc/minute volumetric liquidflow comprising:(a) a flow cell comprising a body means defining anelongate narrow channel; (b) a single electrical resistance heatingmeans and a single companion electrical heat sensing means fixedlyattached in cooperative relationship to the flow cell to alternatelyinput and detect inputted heat pulses in liquid flowing through thechannel; (c) an electrical circuit means to apply a voltage across theheat sensing means to produce a variable electrical analog signalcorresponding to changes in the temperature of the electrical heatsensing means; (d) a differentiating circuit means for receiving theanalog signal, differentiating this signal with respect to time andoutputting a digital pulse signal corresponding to the arrival of eachsuccessive detected heat pulse, said differentiating circuit meanscomprising circuit means for producing an electrical signal which inmagnitude is proportional to the second or a higher order timederivative of the variable electrical analog signal of the heat sensingmeans; (e) an off-on circuit means for applying a pretimed electricalvoltage pulse to the resistance heating means responsive to each digitalpulse outputted by the differentiating circuit means, whereby theoperation of the electrical resistance heating means is triggered byeach successive pulsing of the resistance heating means; (f) saidelongate, narrow channel having a volume corresponding to a calibratedcell volume (V_(c)) which is about 0.5 cc or less.
 6. The apparatus ofclaim 5 wherein the resistance heating means and companion heat sensingmeans comprise a heat emitting probe and a heat sensing probe positioneda fixed distance apart within the channel.
 7. The apparatus of claim 6wherein the heat emitting probe comprises a semiconductor element, andthe heat sensing probe comprising a thermistor element.
 8. The apparatusof claim 7 wherein said probe elements are encased within an insulativecladding material.